10th national competition java test question D: sequence sum

Sequence sum

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Question: After
learning about divisors, Xiao Ming is very curious about divisors. He found that given a positive integer t, we can always find an integer containing t divisors. Xiao Ming is very interested in the smallest number containing t divisors and defines it as St.
For example, S1=1, S2=2, S3=4, S4=6,...
Now Xiao Ming wants to know, when t = 100, what is St?

Idea:
We can first count the prime numbers within 100,000, and then use the knowledge of number theory to find the divisor of a number. We calculate the decomposed prime factor of a number and then add 1 to the exponent of the prime factor and add it to the other The exponent of the prime factor is multiplied by 1 to get the solution of this divisor.
For example:
the prime factor of the decomposition of 6 is 2 3, and the exponent of 2 is (1+1) (1+1) the exponent of 3, so the divisor of 6 is 4,
and then we can find the nearest 100 divisor in the for traversal. Up. Answer: 45360
program:

def z(a):  #判断质数
    if a==2 or a==3:
        return 1
    if a%2==0  or a==1:
        return 0
    k=1
    while k*k<=a:
        k+=2
        if a%k==0:
            return 0
    return 1
b=[]
for p in range(2,100000):
    if z(p):
        b.append(p)
def yu(a):  #a的约数有多少
    s=[]
    i=0
    k=1
    while a!=1:
        if a%b[i]==0:
            a=a//b[i]
            s.append(str(b[i]))
            if z(a):
                s.append(str(a))
                break
        else:
            i+=1
    s1=set(s)
    for i in s1:
        k*=s.count(i)+1
    return k
c=0
while 1:
    c+=1
    if 100==yu(c):
        print(c)
        break

Reprinting is prohibited. Only for self-study. No responsibility for program errors.